JEE Main 2022 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 29 July 2022, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Let A and B be two

3 \times 3

non-zero real matrices such that AB is a zero matrix. Then

(1)the system of linear equations $AX = 0$ has a unique solution
(2)the system of linear equations $AX = 0$ has infinitely many solutionsOfficial answer
(3)B is an invertible matrix
(4) $\operatorname{adj}(A)$ is an invertible matrix

Official answer

Option 2

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Homogeneous System Solutions

Same idea in other shifts

Asked 4× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.